How To Calculate A 90 Confidence Interval By Hand

Calculating a 90% confidence interval by hand is crucial in statistics to estimate the population parameter within a certain degree of confidence. This guide will walk you through the process using our interactive calculator.

1. Enter your sample size, mean, and standard deviation.
2. Click ‘Calculate’.
3. View the results below the calculator.

The formula for calculating a 90% confidence interval is:

CI = x̄ ± Z(1 - α/2) * (s/√n)

Where:

• CI is the confidence interval,
• x̄ is the sample mean,
• Z(1 - α/2) is the Z-score corresponding to the desired confidence level (1.645 for 90%),
• s is the standard deviation,
• n is the sample size.

Comparison of Confidence Intervals

Sample Size	Mean	Standard Deviation	90% Confidence Interval (Manual)	90% Confidence Interval (Using Software)

Z-Scores for Common Confidence Levels

Confidence Level	Z-Score

• Always use the appropriate Z-score for your desired confidence level.
• Ensure your sample size is large enough to provide a reliable estimate.
• Consider using a calculator or software for complex calculations.

What is a confidence interval?

A confidence interval is a range of values around an estimate that indicates the reliability of the estimate.

For more information, see the UK Office for National Statistics and the Centers for Disease Control and Prevention.